American Institute of Mathematical Sciences

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January  2015, 11(1): 199-216. doi: 10.3934/jimo.2015.11.199

Sensor deployment for pipeline leakage detection via optimal boundary control strategies

Chao Xu 1, , Yimeng Dong 1, , Zhigang Ren 1, , Huachen Jiang 2, and  Xin Yu 3,

1. 

State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou, Zhejiang 310027, China, China, China
2. 

Institute of Operations Research & Cybernetics, Zhejiang University, Hangzhou, Zhejiang 310027, China
3. 

Ningbo Institute of Technology, Zhejiang University, Hangzhou, Zhejiang 310027, China

Received  December 2012 Revised  January 2014 Published  May 2014

We consider a multi-agent control problem using PDE techniques for a novel sensing problem arising in the leakage detection and localization of offshore pipelines. A continuous protocol is proposed using parabolic PDEs and then a boundary control law is designed using the maximum principle. Both analytical and numerical solutions of the optimality conditions are studied.
Keywords: Offshore pipeline network, leakage detection, optimal control., continuation approach, multi-agent system, partial differential equations, Lagrangian sensor.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Chao Xu, Yimeng Dong, Zhigang Ren, Huachen Jiang, Xin Yu. Sensor deployment for pipeline leakage detection via optimal boundary control strategies. Journal of Industrial & Management Optimization, 2015, 11 (1) : 199-216. doi: 10.3934/jimo.2015.11.199
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show all references

References:
[1]

North Holland, 1981.  Google Scholar

[2]

Modeling and Simulation in Science, Engineering and Technology. Birkhäuser/Springer, New York, 2011. doi: 10.1007/978-0-8176-8098-5.  Google Scholar

[3]

Kluwer Academic, Dordrecht, 2003. doi: 10.1007/978-94-017-2488-3.  Google Scholar

[4]

IEEE Transactions on Automatic Control, 54 (2009), 2100-2113. doi: 10.1109/TAC.2009.2026934.  Google Scholar

[5]

Mathematics and Computers in Simulation, 64 (2004), 617-630. doi: 10.1016/j.matcom.2003.11.013.  Google Scholar

[6]

Princeton University Press, New York, 2009.  Google Scholar

[7]

in Proceeding of the Conference on Decision and Control, vol. 5, 1999. Google Scholar

[8]

Journal of Industrial and Management Optimization, 8 (2012), 821-840. doi: 10.3934/jimo.2012.8.821.  Google Scholar

[9]

National Bureau of Asian Research, 2010. Google Scholar

[10]

Journal of Hydraulic Engineering-ASCE, 132 (2006), 1215-1228. doi: 10.1061/(ASCE)0733-9429(2006)132:11(1215).  Google Scholar

[11]

Journal of Industrial and Management Optimization, 1 (2005), 499-512. doi: 10.3934/jimo.2005.1.499.  Google Scholar

[12]

Automatica, 44 (2008), 1295-1303. doi: 10.1016/j.automatica.2007.09.024.  Google Scholar

[13]

IEEE Transactions on Automatic Control, 51 (2006), 1058-1063. doi: 10.1109/TAC.2006.876805.  Google Scholar

[14]

IEEE Transactions on Automatic Control, 56 (2011), 1791-1806. doi: 10.1109/TAC.2010.2092210.  Google Scholar

[15]

(Encyclopedia of Mathematics and its Applications) Cambridge University Press, Cambridge, 2008. doi: 10.1017/CBO9780511721595.  Google Scholar

[16]

IEEE Transactions on Automatic Control, 57 (2012), 2688-2694. doi: 10.1109/TAC.2012.2191179.  Google Scholar

[17]

IEEE Transactions on Automatic Control, 56 (2011), 923-929. doi: 10.1109/TAC.2010.2103416.  Google Scholar

[18]

Nonlinear Analysis: Hybrid Systems, 2 (2008), 1152-1167. doi: 10.1016/j.nahs.2008.09.008.  Google Scholar

[19]

Nonlinear Analysis: Hybrid Systems, 4 (2010), 484-495. doi: 10.1016/j.nahs.2009.11.005.  Google Scholar

[20]

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[21]

VDM Verlag, Germany, 2008. Google Scholar

[22]

Journal of Industrial and Management Optimization, 7 (2011), 291-315. doi: 10.3934/jimo.2011.7.291.  Google Scholar

[23]

M. Liu, S. Zang and D. Zhou, Fast leak detection and location of gas pipelines based on an adaptive particle filter,, International Journal of Applied Mathematics and Computer Science, 15 ().   Google Scholar

[24]

Princeton University Press, New York, 2010.  Google Scholar

[25]

Automatica, 47 (2011), 2534-2542. doi: 10.1016/j.automatica.2011.08.045.  Google Scholar

[26]

in Proceeding of the Conference on Decision and Control, 2011, 921-928. Google Scholar

[27]

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[28]

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[29]

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[30]

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[31]

(Communications and Control Engineering Series) Springer-Verlag, London, 2011. Google Scholar

[32]

in Proceedings of the Conference on Decision and Control, 2009, 5139-5144. doi: 10.1109/CDC.2009.5400570.  Google Scholar

[33]

SIAM, Philadephia, 2004. doi: 10.1137/1.9780898717938.  Google Scholar

[34]

American Mathematical Society, New York, 2010.  Google Scholar

[35]

Tsinghua University Press, Beijing, 2010, (In Chinese). Google Scholar

[36]

Control and Instruments in Chemical Industry, 30 (2003), 5-10. Google Scholar

[37]

Nonlinear Dynamics and Systems Theory, 10 (2010), 175-188.  Google Scholar

[38]

Optimal Control Applications and Methods, 33 (2012), 576-594. doi: 10.1002/oca.1015.  Google Scholar

[39]

Journal of Industrial and Management Optimization, 1 (2005), 133-148. doi: 10.3934/jimo.2005.1.133.  Google Scholar

[40]

Journal of Global Optimization, 56 (2013), 503-518. doi: 10.1007/s10898-012-9858-7.  Google Scholar

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